Title

The Generation of Inter-Element-Compatible Stiffness and Mass Matrices by the Use of Interpolation Formulas

Description

This paper presents a general method of subelement displacement states which makes it a relatively simple task to insure completely compatible displacement states. The method involves the use of Hermite interpolation formulas of various order. The total potential energy principle is used to generate stiffness matrices based on these displacement states. The approach is presented in general orthogonal curvilinear coordinates for shell type structures. Inter-element-compatible stiffness matrices are presented for a rectangular membrane, a rectangular plate with twelve degrees of freedom, and a rectangular plate with twenty four degrees of freedom. The corresponding consistent mass matrices are presented for both plate elements. Numerical examples of static deflection analysis are presented based on both of the plate subelements and the monotonic convergence of the discretization error is confirmed. Application of the simpler plate subelement to the determination of natural modes and frequencies is also illustrated with a numerical example. All of the examples are selected so that comparison with classical results can be made.

Date

1966

Index Abstract

Not Available

Photo Quality

Not Needed

Report Number

AFFDL-TR-66-80 p. 395-443

Creator

Bogner, F. K

Fox, R. L.

Schmit, L. A., Jr.

Corporate Author

Case Institute of Technology

Laboratory

Air Force Flight Dynamics Laboratory

Extent

49

Access Rights

Distribution of this document is unlimited.

Distribution Classification

1

Contract

Laboratory Research - No Contract

DTIC Record Exists

No

Distribution Change Authority Correspondence

None

Distribution Conflict

No

Report Availability

Full text available

Date Issued

1966-11

Abstract

This paper presents a general method of subelement displacement states which makes it a relatively simple task to insure completely compatible displacement states. The method involves the use of Hermite interpolation formulas of various order. The total potential energy principle is used to generate stiffness matrices based on these displacement states. The approach is presented in general orthogonal curvilinear coordinates for shell type structures. Inter-element-compatible stiffness matrices are presented for a rectangular membrane, a rectangular plate with twelve degrees of freedom, and a rectangular plate with twenty four degrees of freedom. The corresponding consistent mass matrices are presented for both plate elements. Numerical examples of static deflection analysis are presented based on both of the plate subelements and the monotonic convergence of the discretization error is confirmed. Application of the simpler plate subelement to the determination of natural modes and frequencies is also illustrated with a numerical example. All of the examples are selected so that comparison with classical results can be made.

Identifier

AD0646300

Provenance

Bombardier/Aero

Type

article

Format

1 online resource

Is Referenced By

Castro, S. G. P. & Jansen, E. L. (2022) Displacement-based multi-modal formulation of Koiter’s method applied to cylindrical shells AIAA SCITECH 2022 Forum https://arc.aiaa.org/doi/10.2514/6.2022-0256

Castro, S. G. P. & Jansen, E. L. (2022) Displacement-based multi-modal formulation of Koiter’s method applied to cylindrical shells. Preprint files.osf.io

Mauricio F. Caliri, Jr., Antonio J.M. Ferreira, and Volnei Titac
A new C1 4-node flat laminated shell element based on a generalized plate formulation
v163 (2021): 107648
[Oxford] : Elsevier Applied Science

Ummels, Raphael, & Castro, Saullo G. P. "Overlap-Stiffened Panels for Optimized Buckling Performance Under Minimum Steering Radius Constraints", Preprint DOI
10.31224/osf.io/xpvn4

Ummels, R., & Castro, S. G. P. (2021). Overlap-stiffened panels for optimized buckling performance under
minimum steering radius constraints. Composites Part C: Open Access, 6, [100174].
https://doi.org/10.1016/j.jcomc.2021.100174

Wang, Zhihua, José Humberto S. Almeida Jr., Aravind Ashok, Zhonglai Wang and Saullo G. P. Castro, "Lightweight design of variable-angle filament-wound cylinders combining Kriging-based metamodels with particle swarm optimization", May 12, 2021
https://engrxiv.org/3ym95/

Wang, Zhihua, José Humberto S. Almeida Jr., Aravind Ashok, Zhonglai Wang and Saullo G. P. Castro, "Lightweight design of variable-angle filament-wound cylinders combining Kriging-based metamodels with particle swarm optimization", Structural and Multidisciplinary Optimization, 65:140 (2022)

Is Part Of

Matrix Methods in Structural Mechanics